Lorentz Invariance: Fact or Fiction

Early this year, I won a book contract for a series of science fiction novels. I’m having a huge amount of fun with it, but am plagued by a peculiar anxiety. That people will have issues with my book to do with Lorentz Invariance.

My books are intended to be thinking person’s space opera. There are all those things that people enjoy about science fiction: starships, robots, alien worlds, etc. However, they’re also intended to be at least slightly realistic in the way that they deal with social and scientific themes. And one of the themes that’s used heavily in the books is warp drive.

No matter that SF writers have used warp drive for years, and no matter that the kind of warp drive I use is very similar to the sort that NASA is investigating right now. Still I am plagued with the notion that someone will call me out for apparent causality violations and thus consider the work implausible. Eyebrows will be raised. Readers will flee. Scorn will descend. Etc.

Is this the kind of neurotic thought process that happens when one spends years doing scientific research where you have to justify your every choice, who’s then segueing back into fiction? Absolutely. But here’s the thing: how many people think about Lorentz Invariance is just wrong, and how my books cover it is right and proper. I am filled with shining righteous glee on this subject because Lorentz invariance is a topic that I care about and have researched well beyond the limits of common sense.

The standard argument against faster than light travel goes something like this: travel faster than light in your reference frame and you’re going backward in time in someone else’s. Thus if you travel faster than light, you’ve broken causality. No. This is what drives me crazy. Wrong. Bad. A conclusion based on false assumptions. The person who believes this gets ten minutes in the naughty corner. With a novelty hat on.

This belief gets such a strong reaction from me because there are many science fiction writers who believe it is true. Including some very notable ones who have worked in physics. They pat themselves on the back for being science-savvy and diligently write books that preclude FTL. Gah!

It is true that if you travel faster than light, something about your experience of the universe breaks, but it doesn’t have to be causality. There is another, perfectly natural way that our experience of spacetime might change which is in perfect keeping with the math. It is this: travel faster than light, and you break Lorentz Invariance. In other words, all reference frames don’t look the same any more.

This is my preferred model, not only because it works, but because I think there’s evidence that this is what would actually happen. Why? For starters, there is one reference frame that Nature has pulled out and made screamingly special for us already: the one defined by the CMB. While this fact doesn’t interfere with how we do physics, it reveals that the observable universe started with a specific frame. Furthermore, there is no evidence that bits of the universe far away from us are traveling wildly, randomly fast compared to us, suggesting that the entire universe shares that same frame.

Given this, in order for Lorentz invariance to be strictly true, the vast majority of possible reference frames would have to be ones in which the universe hasn’t started yet and is totally flat, i.e.: two-dimensional. This is because no matter how close you get to the speed of light, you can always go closer. This means that for almost all possible frames, nothing can have possibly happened, as the duration of the universe to date is less than the Planck length. Can we honestly say that those frames exist if the universe hasn’t started in them yet?

Most of the available frames are ones that we could never even reach, because even if you totaled up all the energy in the universe and used it to push a single particle to some absurdly high speed, there would still be an endless spread of reference frames beyond it, all exactly equivalent and immaculately unreachable. Thus, even if you go for an infinite universe model such as eternal inflation, almost all possible frames will never be used. The local energy density at any point will never be high enough to make things pan out otherwise.

So the simple fact that the universe has a starting frame means that Lorentz invariance can only ever be measured to be locally true. It is also true that finite, discrete universe models (my favorites) only work if Lorentz invariance does not strictly hold. That’s true even if you build your discrete universe out of some nice Minkowski-metric compatible structure such as causal sets. Something can only be truly Lorentz invariant if it has infinite size, and exists for infinite time.

So given that strict Lorentz invariance is outlandish enough that we could never even prove that it held were it true, all possible models that can encompass local Lorentz invariance must be considered equally valid. Thus, holding physical reality to the absurd requirement of resembling Minkowski-space simply because it’s where we do most of the math that people are used to seems ludicrous to me.

There is a lovely upside to all this. While we have no evidence that anything in nature can go faster than light, there is also nothing in relativity that rules it out. Which means that NASA’s experiments with an Alcubierre drive may yet bear fruit. And that’s something worth being truly optimistic about.

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Just because we assume that all reference frames are equally valid doesn’t mean we have to assume that we’re equally likely to find ourselves in all reference frames. So what if the vast majority of possible reference frames are effectively decoupled from us? This strikes me as similar to arguments about the probability of physical laws or fundamental constants having the form they are in our universe, when we have a sample size of one and our intuitions about probability shouldn’t be extrapolated to the laws of physics. (Physicists generally end up falling back on: (1) something like string theory, which makes the laws inevitable, except for choosing among the 10^500 versions of string theory; (b) some combination of the anthropic principle and the multiverse.) But what if the laws are what they are and the vast majority of matter happens to be in a given reference frame just because they are? Until we can gather evidence for an alternative, it’s mere philosophical speculation about which theory we find most aesthetically appealing.

Fair point, but I suppose my concern is this: let’s say you have a set of theories X, Y, and Z that concern a phenomenon P. People like X because it makes the math easy, so everyone gets trained in X. Then someone comes up with a hypothetical case S of P which X rules out but Y and Z do not. Is it scientifically appropriate to discard S and not research it because X rules it out? I think not. Sure, it makes S less likely to pan out, but surely that makes it more scientifically important, because science advances through refutation. This makes the issue one of science policy, not abstract philosophy. Given how much scientific reasoning in relativity depends on the Minkowski metric, doesn’t it justify experimental efforts to exclude it from realistic models of spacetime?

Zack S

May 19, 2014 at 11:51 pm

OK, so what are these experimental / observational efforts that we’re not making (aside from trying to build warp drive itself) that would disprove Minkowski / Lorentz invariance but be consistent with existing data?

Also, I feel compelled to say, if making the math easier is really a big selling point for a theory (as has sometimes been good guidance in the last few hundred years of physics), then string theorists are really doing it wrong!

Re string theory: agreed. Mind you, the kind of alternative I’m suggesting admittedly uses a compact dimension to code for spacetime interval, or some equivalent mechanism. So you have to invoke some of the same ideas that string theorists use to get the non-Minkowski spacetime model to work. 😦 As for experimental/observational efforts, I guess what I’d like to see is just a lot more mucking about with warp drive. But if I had a free billion dollars to throw at warp drive research, I’d give some to aid the holometer project and some for neutrino oscillation experiments or anything related to the Higgs. If I had to bet, I would say that understanding the weak force properly would be the way to go to crack warp. You can’t understand relativity until you understand mass. And frankly, we don’t yet. I’m not a physicist, as I often remind people on this blog, but I’ve gone past feeling humble about that. There’s so much physics research time and effort that gets dumped into pointless shit. People don’t put money behind things like warp drive because for most it’s a career-killer.

This reminds me of something I thought of the other week. A photon leaving the surface of the sun and eight minutes later (as far as I’m concerned from my frame of reference) hitting the retina of my eye, in it’s frame of reference has instantaneously traveled from the sun to my eye. Similarly a photon generated at the birth of the universe and heading outwards for billions of years, defining the edge of the universe until the latter collapses in on itself makes the journey in no time at all according to its frame of reference. So all photons think they are the same age, no matter how long they actually are in existence for as far as I am concerned.